1. Field of the Invention
The invention relates generally to the field of seismic surveying of subsurface Earth formations. More specifically, the invention relates to methods for prestack migration of seismic data in which amplitudes of events in the seismic data are substantially preserved.
2. Background Art
Seismic surveying is used to evaluate structures of, compositions of, and fluid content of subsurface earth formations. A particular application for seismic surveying is to infer the presence of useful materials, such as petroleum, in the subsurface earth formations. Generally, seismic surveying includes deploying an array of seismic sensors at or near the earth's surface, and deploying a seismic energy source or an array of such sources also at or near the surface. The seismic energy source is actuated and seismic energy emanates from the source, traveling generally downwardly through the subsurface until it reaches one or more acoustic impedance boundaries in the subsurface. Seismic energy is reflected from the one or more impedance boundaries, where it then travels upwardly until being detected by one or more of the sensors. Structure and composition of the Earth's subsurface is inferred from, among other properties of the detected energy, the travel time of the seismic energy, and the amplitude and phase of the various frequency components of the seismic energy with respect to the energy emanating from the seismic source.
In order to infer the structures of subsurface earth formations from seismic travel times measured at or near the earth's surface from a source position at or near the surface, it is necessary to determine the velocity of the various formations through which the seismic energy passes. Velocities of the earth formations can vary both with respect to depth in the earth (vertically), and with respect to geographic position (laterally). Seismic data, however, are recorded only with respect to time. Methods known in the art for estimating velocities of the earth formations both vertically and laterally rely on inferences about the travel path geometry of the seismic energy as it travels from the seismic source to the various seismic receivers deployed at the earth's surface.
In order for images produced from seismic data to correspond accurately to the spatial distribution of subsurface structures and compositional changes in the Earth's subsurface, techniques known generally as “time migration” and “depth migration” are performed on the seismic data. Migration is a process by which reflection events in seismic data are made to correspond to their true spatial position. Time migration positions the reflective events in time and does not correct for all effects of lateral velocity gradients. Depth migration attempts to place reflective events at their true depth positions within the Earth's subsurface.
There are generally two classes of time migration techniques. One type of time migration is known as prestack time migration and disclosed, for example, in, Sun, C., Martinez, R., Amplitude preserving 3D pre-stack Kirchhoff time migration for V(z) and VTI media, 72nd Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, pp. 1224–1227 (2002). Pre-stack migration is performed on individual seismic data recordings (“traces”) and can be computationally expensive.
The other type of time migration is called post stack migration, which represents migration techniques that are performed on seismic data for which numbers of individual data recordings are summed (“stacked”) to improve signal to noise ratio. Prestack migration typically produces better images, although it is computationally more expensive than post-stack migration.
The prestack time migration method disclosed in the Sun et al. paper mentioned above is one of a type known as “amplitude preserving”, meaning that the amplitudes of events in the seismic data are substantially preserved during the migration procedure. Amplitude preserving migration provides, among other benefits, greater accuracy in processing techniques known as “amplitude versus offset” (AVO). A principal objective of amplitude preserving migration techniques is to make the reflection amplitudes proportional to the reflectivity at the various subsurface boundaries. Amplitude preserving migration is thus characterized by recovering amplitude loss in reflected seismic energy caused by geometric spreading of the seismic energy during propagation through the Earth, so that the amplitudes at least to some extent correspond to the reflectivity of the various subsurface boundaries.
A prestack migrated image is calculated by mapping contributing data samples of an input seismic data trace to a target sample of an image trace, subject to the constraint that the contributing data sample time (indexed to actuation of the seismic source) is the same as the travel time of seismic energy from the seismic source to the receiver via the image point. The contributing data samples from all the input seismic data traces are then summed. A so-called “true amplitude” migration, which recovers the reflection amplitude loss caused by geometric spreading so that the amplitudes correspond to the reflectivity of subsurface reflectors, is achieved by a weighted, rather than a simple summation of the input data samples. That is, the amplitude of the contributing data sample represents the sum of the input data samples multiplied by a weighting factor. The weighting factor is a function of a number of different variables, including the travel time, and the locations of the source and receiver corresponding to each data sample trace (called the “acquisition geometry”). There are several different techniques for determining “true amplitude” weight function known in the art. See, for example, Schleicher, J., Tygel, M., and Hubral, P., 1993, 3-D true amplitude finite-offset migration; Geophysics, 58, 1112–1126, or Bleistein, N., Cohen, J. K., Stockwell, J. W., Mathematics of multidimensional seismic imaging, migration, and inversion, Springer, 2001. The true amplitude weight functions for the most common seismic data acquisition geometries, such as common-shot or common-offset geometry, contain terms which include square roots of the cosine of the takeoff and emergence angles, and in-plane and out-of-plane spreading terms for every possible combination of source, receiver, and image point, even for the relatively simple case of a v(z) medium. See, for example, Zhang, Y., Gray, S., Young, J., Exact and approximate weights for Kirchhoff migration, 70th Annual Internat. Mtg., Soc. Expl. Geophys. Expanded Abstracts, 1036–1039 (2000). Because the generation of the weights is very computationally demanding and the weights must be stored and interpolated during migration, the computation of the weight function can dominate the total computation cost of the migration process.
It is known in the art to approximate the weight function in various ways so as to avoid increased input/output and computational expense. See, for example, Dellinger, J. A., Gray, S. H., Murphy, G. E., and Etgen, J. T., Efficient 2.5-D true-amplitude migration; Geophysics, 65, 943–950 (2000). Typically such estimates are made using a constant velocity approximation for the Earth formations. However, it has been determined that weight functions estimated using the constant velocity approximation frequently do not provide satisfactory results for processing called “amplitude versus offset” (“AVO”) in v(z) (velocity varies with depth) media. There exists a need for a prestack migration technique that provides amplitude quality similar to those provided by “exact” true-amplitude techniques known in the art, yet does not require significant increase of computational expense.